Find the area of the sector of a circle of radius 5 cm if the corresponding arc length is 3.5 cm.
\(8.75\,\text{cm}^2\)
Step 1: Recall the formula for the area of a sector when the arc length is given:
\[ A = \tfrac{1}{2} \times r \times l \]
Here, \(r\) = radius of the circle, and \(l\) = arc length.
Step 2: Write down the values from the question:
Step 3: Substitute these values into the formula:
\[ A = \tfrac{1}{2} \times 5 \times 3.5 \]
Step 4: First multiply radius and arc length:
\[ 5 \times 3.5 = 17.5 \]
Step 5: Now divide by 2:
\[ \tfrac{17.5}{2} = 8.75 \]
Final Answer: \(A = 8.75\,\text{cm}^2\)
So, the area of the sector is 8.75 square centimetres.